If test voltages with a volt meter when either the fuse on this circuit is blown or ground is not connected to the battery, then I read the 12V battery voltage on both the input of the 7805 voltage regulator and the output. I don't really understand why this is so but it must have something to do with the meter ground being connected to the battery ground.

If the fuse is good and the board is connected to the battery ground then everything reads fine (e.g. 5V on the 7805 output).

Can someone explain why the 12V on the output of the 7805 is observed in this case?

It's because the impedance of your meter is so high. Any leakage at all through the diode, and you will see the battery potential at the regulator output; as without a ground path there is no load on the board.

have you tried removing the diode?
i have a feeling the reverse biasing might be why, dont quote me on it

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The diode is to discharge the output of the regulator when the external supply is removed. If you reverse it, the diode will conduct in normal operation... not good! Then you'd raise the 5V rail up close to the input (12V??).

I suspect that without a gnd reference, your regulator has nothing to regulate voltage against. The ground pin will drift high (possibly quickly) and the regulator follows. Measure your return to battery negative and see if you don't get the same 12v.